A paradox is a seemingly absurd or impossible concept, proposition, or theory that is often difficult to understand or explain, sometimes apparently self-contradictory, and yet ultimately correct or true. How is it possible, for example, that oxygen "a toxic environmental poison" could be also indispensable for life (Beckman and Ames Physiol Rev 78(2):547-81, 1998; Stadtman and Berlett Chem Res Toxicol 10(5):485-94, 1997)?: the so-called Oxygen Paradox (Davies and Ursini 1995; Davies Biochem Soc Symp 61:1-31, 1995). How can French people apparently disregard the rule that high dietary intakes of cholesterol and saturated fats (e.g., cheese and paté) will result in an early death from cardiovascular diseases (Renaud and de Lorgeril Lancet 339(8808):1523-6, 1992; Catalgol et al. Front Pharmacol 3:141, 2012; Eisenberg et al. Nat Med 22(12):1428-1438, 2016)?: the so-called, French Paradox. Doubtless, the truth is not a duality and epistemological bias probably generates apparently self-contradictory conclusions. Perhaps nowhere in biology are there so many apparently contradictory views, and even experimental results, affecting human physiology and pathology as in the fields of free radicals and oxidative stress, antioxidants, foods and drinks, and dietary recommendations; this is particularly true when issues such as disease-susceptibility or avoidance, "healthspan," "lifespan," and ageing are involved. Consider, for example, the apparently paradoxical observation that treatment with low doses of a substance that is toxic at high concentrations may actually induce transient adaptations that protect against a subsequent exposure to the same (or similar) toxin. This particular paradox is now mechanistically explained as "Adaptive Homeostasis" (Davies Mol Asp Med 49:1-7, 2016; Pomatto et al. 2017a; Lomeli et al. Clin Sci (Lond) 131(21):2573-2599, 2017; Pomatto and Davies 2017); the non-damaging process by which an apparent toxicant can activate biological signal transduction pathways to increase expression of protective genes, by mechanisms that are completely different from those by which the same agent induces toxicity at high concentrations. In this review, we explore the influences and effects of paradoxes such as the Oxygen Paradox and the French Paradox on the etiology, progression, and outcomes of many of the major human age-related diseases, as well as the basic biological phenomenon of ageing itself.